Trigonometric Ratios practice questions

Trigonometric Ratios questions

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1. 1Trigonometric ratiosStandard

   In a right triangle, the side opposite angle A has length 3 and the hypotenuse has length 5. What is sin A?In a right triangle, the side opposite angle A has length 3 and the hypotenuse has length 5. What is sin A?

   • A353/5
   • B454/5
   • C343/4
   • D535/3
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   Answer: 353/5

   Sine is the ratio of the opposite side to the hypotenuse, which is 35.Sine is the ratio of the opposite side to the hypotenuse, which is 3/5.

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2. 2Trigonometric ratiosStandard

   In a right triangle, the leg opposite angle B has length 7 and the leg adjacent to angle B has length 24. What is tan B?In a right triangle, the leg opposite angle B has length 7 and the leg adjacent to angle B has length 24. What is tan B?

   • A7247/24
   • B24724/7
   • C7257/25
   • D242524/25
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   Answer: 7247/24

   Tangent is the ratio of the opposite leg to the adjacent leg, which is 724. The hypotenuse is not used.Tangent is the ratio of the opposite leg to the adjacent leg, which is 7/24. The hypotenuse is not used.

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3. 3Trigonometric ratiosStandard

   In a right triangle, the legs measure 8 and 15. What is the cosine of the angle adjacent to the leg of length 8?In a right triangle, the legs measure 8 and 15. What is the cosine of the angle adjacent to the leg of length 8?

   • A15815/8
   • B8178/17
   • C8158/15
   • D151715/17
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   Answer: 8178/17

   The hypotenuse is √64 + 225 = √289 = 17. Cosine is the adjacent leg over the hypotenuse, and the leg adjacent to that angle is 8, giving 817.The hypotenuse is √(64 + 225) = √(289) = 17. Cosine is the adjacent leg over the hypotenuse, and the leg adjacent to that angle is 8, giving 8/17.

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4. 4Trigonometric ratiosStandard

   In a right triangle with the right angle at C, side a = 6 and side b = 8. What is sin A, where a is opposite angle A?In a right triangle with the right angle at C, side a = 6 and side b = 8. What is sin A, where a is opposite angle A?

   • A0.750.75
   • B0.80.8
   • C1.251.25
   • D0.60.6
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   Answer: 0.60.6

   The hypotenuse is √36 + 64 = 10. Sine is the opposite side over the hypotenuse: 610 = 0.6.The hypotenuse is √(36 + 64) = 10. Sine is the opposite side over the hypotenuse: 6/10 = 0.6.

   How did you do?Got itMissed it
5. 5Trigonometric ratiosStandard

   In right triangle ABC the right angle is at B, AB = 8 and BC = 15, so AC = 17. What is sin A?In right triangle ABC the right angle is at B, AB = 8 and BC = 15, so AC = 17. What is sin A?

   • A8178/17
   • B15815/8
   • C151715/17
   • D8158/15
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   Answer: 151715/17

   Sine is opposite over hypotenuse. The side opposite angle A is BC = 15 and the hypotenuse is AC = 17, so sin A = 1517. The choice 817 is cos A, taken from the side next to the angle rather than across from it.Sine is opposite over hypotenuse. The side opposite angle A is BC = 15 and the hypotenuse is AC = 17, so sin A = 15/17. The choice 8/17 is cos A, taken from the side next to the angle rather than across from it.

   How did you do?Got itMissed it
6. 6Trigonometric ratiosStandard

   In a right triangle, the side adjacent to angle theta is 12 and the hypotenuse is 13. What is cos theta?In a right triangle, the side adjacent to angle theta is 12 and the hypotenuse is 13. What is cos theta?

   • A5135/13
   • B5125/12
   • C121312/13
   • D131213/12
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   Answer: 121312/13

   Cosine is adjacent over hypotenuse, so 1213. The remaining side is 5, making 513 the sine and 512 the tangent — all three are available, and the question asks for one.Cosine is adjacent over hypotenuse, so 12/13. The remaining side is 5, making 5/13 the sine and 5/12 the tangent — all three are available, and the question asks for one.

   How did you do?Got itMissed it
7. 7Trigonometric ratiosStandard

   In a right triangle, the side opposite angle theta is 9 and the hypotenuse is 15. What is sin theta?In a right triangle, the side opposite angle theta is 9 and the hypotenuse is 15. What is sin theta?

   • A454/5
   • B343/4
   • C353/5
   • D535/3
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   Answer: 353/5

   Sine is opposite over hypotenuse: 915 = 35. The remaining side is 12, making 45 the cosine and 34 the tangent — all three are available and the question asks for one.Sine is opposite over hypotenuse: 9/15 = 3/5. The remaining side is 12, making 4/5 the cosine and 3/4 the tangent — all three are available and the question asks for one.

   How did you do?Got itMissed it
8. 8Trigonometric ratiosChallenge

   In a right triangle, angle A and angle B are the two acute angles. If sin A = 0.6, what is cos B?In a right triangle, angle A and angle B are the two acute angles. If sin A = 0.6, what is cos B?

   • A1.61.6
   • B0.60.6
   • C0.40.4
   • D0.80.8
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   Answer: 0.60.6

   The two acute angles in a right triangle are complementary, and sin(x) = cos(90 - x). Because B = 90 - A, cos B equals sin A, which is 0.6.The two acute angles in a right triangle are complementary, and sin(x) = cos(90 - x). Because B = 90 - A, cos B equals sin A, which is 0.6.

   How did you do?Got itMissed it
9. 9Trigonometric ratiosChallenge

   In a right triangle, tan A = 34. What is sin A?In a right triangle, tan A = 3/4. What is sin A?

   • A353/5
   • B454/5
   • C535/3
   • D343/4
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   Answer: 353/5

   Tangent 34 means the opposite and adjacent sides are in the ratio 3 to 4, which makes the hypotenuse 5 by the Pythagorean theorem. Sine is opposite over hypotenuse, so 35.Tangent 3/4 means the opposite and adjacent sides are in the ratio 3 to 4, which makes the hypotenuse 5 by the Pythagorean theorem. Sine is opposite over hypotenuse, so 3/5.

   How did you do?Got itMissed it
10. 10Trigonometric ratiosChallenge

    In a right triangle, cos B = 513. What is tan B?In a right triangle, cos B = 5/13. What is tan B?

    • A13513/5
    • B12512/5
    • C5125/12
    • D121312/13
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    Answer: 12512/5

    Cosine 513 means the adjacent side is 5 and the hypotenuse 13, so the opposite side is 12 by the Pythagorean theorem. Tangent is opposite over adjacent, giving 125.Cosine 5/13 means the adjacent side is 5 and the hypotenuse 13, so the opposite side is 12 by the Pythagorean theorem. Tangent is opposite over adjacent, giving 12/5.

    How did you do?Got itMissed it
11. 11Trigonometric ratiosChallenge

    In a right triangle, the tangent of angle theta is 34 and the side opposite theta has length 9. What is the length of the side adjacent to theta?In a right triangle, the tangent of angle theta is 3/4 and the side opposite theta has length 9. What is the length of the side adjacent to theta?

    • A6.756.75
    • B1515
    • C33
    • D1212
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    Answer: 1212

    Tangent is opposite over adjacent, so 9 / adjacent = 34 and adjacent = 9(43) = 12. Multiplying by 34 instead of dividing gives 6.75, and 15 is the hypotenuse of the 9-12-15 triangle this turns out to be.Tangent is opposite over adjacent, so 9 / adjacent = 3/4 and adjacent = 9(4/3) = 12. Multiplying by 3/4 instead of dividing gives 6.75, and 15 is the hypotenuse of the 9-12-15 triangle this turns out to be.

    How did you do?Got itMissed it